On monotone and pointwise splittability
Lj. Kočinac (1991)
Matematički Vesnik
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Lj. Kočinac (1991)
Matematički Vesnik
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Kvinikadze, G. (1999)
Memoirs on Differential Equations and Mathematical Physics
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Noboru Endou (2015)
Formalized Mathematics
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In this article we introduce the convergence of extended realvalued double sequences [16], [17]. It is similar to our previous articles [15], [10]. In addition, we also prove Fatou’s lemma and the monotone convergence theorem for double sequences.
Andrzej Smajdor (2006)
Annales Polonici Mathematici
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We define absolutely monotone multifunctions and prove their analyticity on an interval [0,b).
Marko Švec (1967)
Colloquium Mathematicae
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Cabada, Alberto, Nieto, Juan J., Heikkilä, Seppo (1998)
International Journal of Mathematics and Mathematical Sciences
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Philip Hartman (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Ian Stares (1995)
Commentationes Mathematicae Universitatis Carolinae
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We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of -spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.
Aleš Nekvinda, Ondřej Zindulka (2011)
Fundamenta Mathematicae
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A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.
Nikolaos S. Papageorgiou (1991)
Publications de l'Institut Mathématique
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Volle, M. (1994)
Journal of Convex Analysis
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